To conclude this section, we can interpret the functor \(Re\) —and because of Proposition REF  also the functor \(S_e\) —in the context of the cohesive \(\infty \) -topos \({\mathbf {H}}\)  of presheaves of spaces on \({{C}\mathrm {art}}\)  as follows (see [1]} for more background).
From the proof of Proposition REF  we see that there are canonical weak equivalences
\(Re \circ Q^p (F) &\cong B^{\Delta {T}\mathrm {op}}(F, {{C}\mathrm {art}}, \mathrm {D})\\&\simeq B^{\Delta {T}\mathrm {op}}(F, {{C}\mathrm {art}}, *)\\&\cong \big | B^{{S}\mathrm {et}_{\hspace{-0.85355pt}\Delta }}(F, {{C}\mathrm {art}}, *) \big |\,.\) 
